Properties of a Generalized Diversity Index

Diversity indices attempt to summarize both the total number of species in a population and the degree of evenness of the species relative abundances. A general diversity index,H(α, β), was proposed by Good (1953) and defined for α and β non-negative integers. For example,H(1, 1) andH(2, 0) are two popular diversity indices due to Shannon (1948) and Simpson (1949) respectively. This paper presents results extending α and β to include any real values under two desirable properties due to Pielou (1975). The evenness and richness components of diversity have been examined and optimal choices of α and β discussed, particularly for the equiprobable and broken-stick models of abundance.